Related papers: Optimization-Based Algebraic Multigrid Coarsening …

Finding optimal bidding strategies for generation units in electricity markets would result in higher profit. However, it is a challenging problem due to the system uncertainty which is due to the unknown other generation units' strategies.…

Continual Graph Learning (CGL) enables models to incrementally learn from streaming graph-structured data without forgetting previously acquired knowledge. Experience replay is a common solution that reuses a subset of past samples during…

In recent years, graph neural networks (GNNs) have been widely applied in tackling combinatorial optimization problems. However, existing methods still suffer from limited accuracy when addressing that on complex graphs and exhibit poor…

Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is well-understood in terms of the $A$-norm, but in a nonsymmetric…

Hybridizing machine learning techniques with metaheuristics has attracted significant attention in recent years. Many attempts employ supervised or reinforcement learning to support the decision-making of heuristic methods. However, in some…

Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large sparse system of equations. However, how to build/check restriction and prolongation operators in practical of AMG methods for nonsymmetric {\em…

Hierarchical abstractions are a methodology for solving large-scale graph problems in various disciplines. Coarsening is one such approach: it generates a pyramid of graphs whereby the one in the next level is a structural summary of the…

Image reconstruction by Algebraic Methods (AM) outperforms the transform methods in situations where the data collection procedure is constrained by time, space, and radiation dose. AM algorithms can also be applied for the cases where…

Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters,…

Large Language Models (LLMs) increasingly rely on agentic capabilities-iterative retrieval, tool use, and decision-making-to overcome the limits of static, parametric knowledge. Yet existing agentic frameworks treat external information as…

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it…

In graph-structured multi-agent reinforcement learning (MARL) adversarial tasks such as pursuit and confrontation, agents must coordinate under highly dynamic interactions, where sparse rewards hinder efficient policy learning. We propose…

One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural…

Multi-sourced datasets are common in studies of variable interactions, for example, individual-level fMRI integration, cross-domain recommendation, etc, where each source induces a related but distinct dependency structure. Joint learning…

Link prediction is a fundamental problem in many graph based applications, such as protein-protein interaction prediction. Graph neural network (GNN) has recently been widely used for link prediction. However, existing GNN based link…

Despite the strong abilities, large language models (LLMs) still suffer from hallucinations and reliance on outdated knowledge, raising concerns in knowledge-intensive tasks. Graph-based retrieval-augmented generation (GRAG) enriches LLMs…

Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough…

Coarse-graining (CG) enables molecular dynamics (MD) simulations of larger systems and longer timescales that are otherwise infeasible with atomistic models. Machine learning potentials (MLPs), with their capacity to capture many-body…

Graph Retrieval-Augmented Generation (GraphRAG) has shown great effectiveness in enhancing the reasoning abilities of LLMs by leveraging graph structures for knowledge representation and modeling complex real-world relationships. However,…

Retrieval-Augmented Generation (RAG) is widely used to mitigate hallucinations of Large Language Models (LLMs) by leveraging external knowledge. While effective for simple queries, traditional RAG systems struggle with large-scale,…